Topology/Quotient Spaces

Let $(X,\tau )$ be a topological space, and let $\sim$ be an equivalence relation on $X$.

Let $X^{*}$ be the partition of $X$ associated to $\sim$.

For $U\in \tau$, define $U^{*}$ to be the set of equivalence classes of all the elements in $U$, and let ${\tau }^{*}=\{U^{*}:U\in \tau \}$.

Then $\tau$ is the quotient topology for the quotient space $(X^{*},{\tau }^{*})$.